Art and theme are two obvious weak spots for me. Quite often the theme doesn’t even need to be important if it’s enough to make something seem more interesting. Welcome To is such a nice piece of paper to look at which drew me in initially, while I opted for Barenpark over Patchwork purely because it had bears instead of a quilt. I was sold on Imperial Settlers over 51st State due to art AND theme.
I think another weakpoint is when novelty meets functionality. By that I mean when a designer might do something slightly different, but it actually works. Chronicles of Crime’s QR codes and Taverns of Tiefenthal’s jigsaw-like player board spring instantly to mind.
As I play mostly with my girlfriend, I also have a weakspot for two-player only games. So I opt for 7 Wonders Duel over 7 Wonders and Agricola ACBAS over the other versions. Targi over any other off-puttingly beige looking game.